May the same numerical optimizer be used when searching either for the best or for the worst solution to a real-world problem?

Adam P. Piotrowski , Maciej Jarosław Napiórkowski


Over the last two decades numerous metaheuristics have been proposed and it seems today that nobody is able to understand, evaluate, or compare them all. In principle, optimization methods, including the recently popular Evolutionary Computation or Swarm Intelligence-based ones, should be developed in order to solve real-world problems. Yet the vast majority of metaheuristics are tested in the source papers on artificial benchmarks only, so their usefulness for various practical applications remains unverified. As a result, choosing the proper method for a particular real-world problem is a difficult task. This paper shows that such a choice is even more complicated if one wishes, with good reason, to use metaheuristics twice, once to find the best and then to find the worst solutions for the specific numerical real-world problem. It often occurs that for either case different optimizers are to be recommended. The above finding is based on testing 30 metaheuristics on numerical real-world problems from CEC2011. First we solve 22 minimization problems as defined for CEC2011. Then we reverse the objective function for each problem and search for its maximizing solution. We also observe that algorithms that are highly ranked on average may not perform best for any given specific problem. Rather, the highest average ranking may be achieved by methods that are never among the poorest ones. In other words, occasional winners may get less attention than rare losers.
Author Adam P. Piotrowski
Adam P. Piotrowski,,
, Maciej Jarosław Napiórkowski ZIBJŚ
Maciej Jarosław Napiórkowski,,
- Department of Informationa Science and Environment Quality Research
Journal seriesInformation Sciences, ISSN 0020-0255
Issue year2016
Publication size in sheets1.2
Keywords in EnglishMetaheuristic, Continuous real-world problem, No Free Lunch, Genetic algorithm, Differential Evolution, Particle Swarm Optimization
Languageen angielski
1-s2.0-S0020025516306296-main.pdf 7.64 MB
Score (nominal)45
ScoreMinisterial score = 45.0, 28-11-2017, ArticleFromJournal
Ministerial score (2013-2016) = 45.0, 28-11-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 4.832 (2) - 2016=4.732 (5)
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.